It’s a big decision. The House lawmakers would have to forgo running for re-election in November if they enter the Senate race, since candidates cannot run simultaneously for more than one federal office in Oklahoma, said Keith Gaddie, a political science professor at the University of Oklahoma. Mr. Pruitt would also not be eligible to run for re-election in 2014 if he competes for Mr. Coburn’s seat, Mr. Gaddie said.

“If you declare for this and file for it, it’s a one-way trip,” Mr. Gaddie said. That may cause Mr. Cole to hesitate before jumping into the Senate race, given his stature in the House and the challenge he would face competing against the GOP field, Mr. Gaddie said.

“He’s too powerful in the House,” he said. “For an old-school Republican, it’s just too tough a primary.”

Now in his sixth House term, Mr. Cole is the most senior of the lawmakers, but represents a more centrist district, including part of Oklahoma City.

“Tom Cole will be seen as a moderate Republican,” said Gretchen Hamel, a GOP strategist and Oklahoma native.

On Friday, the three lawmakers and Mr. Pruitt all put out statements praising Mr. Coburn’s tenure in Washington, but either declined to comment on their Senate intentions or did not immediately respond to requests for comment.

Democrats stand little chance of capturing Mr. Coburn’s seat in a state where GOP presidential nominee Mitt Romney claimed 66.8% of the state’s votes in 2012. Oklahoma’s senior senator, Republican James Inhofe is expected to easily win re-election in 2014. The last Oklahoma Democrat in the Senate was David Boren, who stepped down in 1994 to become the University of Oklahoma’s president.

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